On a property of special groups
Zinovy Reichstein and Boris Youssin
Let $G$ be an algebraic group defined over an algebraically closed field $k$ of characteristic zero. We give a simple proof of the following result: if $H^1(K_0, G) = \{1\}$ for some finitely generated field extension $K_0/k$ of transcendence degree $\geq 3$ then $H^1(K, G) = \{1\}$ for every field extension $K/k$.